Growing up in Rockville Centre, Stevenson befriended members of The Arrogant Sons of Bitches. After they disbanded in 2005, she was appointed keyboard player for the lead singer Jeff Rosenstock's new project, Bomb The Music Industry!. At this point, she had written a number of songs and was performing solo. While recording and touring with Bomb The Music Industry!, she began to piece together her own band, which was named Laura Stevenson & the Cans.

Initially, Stevenson's band consisted primarily of members of Bomb The Music Industry!. In summer 2007, Stevenson recruited Michael Campbell of the Long Islandpunk band Latterman to play bass guitar for The Cans.[1]Alex Billig was added on trumpet later that fall, and a year later Stevenson began working on her first studio recording.

Asian Man Records released "A Record" on April 13, 2010, on LP and CD. The group spent more than half of that year on tour in The United States, Canada, the United Kingdom and Western Europe in various line-ups: sometimes as small as just Stevenson and Campbell on acoustic guitars, and other times fully electric with a three-piece horn section. The group toured with Bomb The Music Industry!, Maps & Atlases, Cults, and Cheap Girls.

Stevenson's third full length album, Wheel, was released on April 23, 2013, on Don Giovanni Records. Pitchfork Media had previously premiered the first single from the album, "Runner".[4] Stevenson toured the U.S. in April and May in support of the album along with another New York band, Field Mouse.